113 4.5.1 Développement asymptotique de la solution ,
117 4.6.1 L'opérateur Dirichlet-to, p.119 ,
Handbook of mathematical functions Dover Publications, 1965. ,
Simulation of corona discharge in point???plane configuration, Journal of Electrostatics, vol.61, issue.2, pp.85-98, 2004. ,
DOI : 10.1016/j.elstat.2004.01.021
Coulomb Simulation of corona discharge in configuration with a sharp electrode, J. of Optoelectronics and Advanced Materials, vol.6, pp.1023-1028, 2004. ,
Approximations of solutions and singularities coefficients for an elliptic problem in a polygonal domain, 1989. ,
Dirichlet and Neumann exterior problems for the n-dimensional Laplace operator. An approch in weighted Sobolev spaces, J. Math ,
Laplace equation in the half space with a non homogenous boundary condition, Mathematica Bohemica, vol.2, pp.265-274, 2001. ,
The Neumann problem in the half-space, Comptes Rendus Mathematique, vol.335, issue.2, pp.151-156, 2002. ,
DOI : 10.1016/S1631-073X(02)02428-7
Elliptic Problems in Domains with Edges: Anisotropic Regularity and Anisotropic Finite Element Meshes, Advances in Numerical Mathematics, 1994. ,
DOI : 10.1007/978-1-4612-2436-5_2
The finite element method with anisotropic mesh grading for elliptic problems in domains with corners and edges, Mathematical Methods in the Applied Sciences, vol.9, issue.6, pp.519-549, 1998. ,
DOI : 10.1002/(SICI)1099-1476(199804)21:6<519::AID-MMA962>3.0.CO;2-R
Vlasov-Maxwell Simulations in Singular Geometries, Lecture Notes in Computer Science, vol.3994, pp.623-630, 2006. ,
DOI : 10.1007/11758549_85
Theoretical tools to solve the axisymmetric Maxwell equations, Mathematical Methods in the Applied Sciences, vol.161, issue.1, pp.49-78, 2002. ,
DOI : 10.1002/mma.279
URL : https://hal.archives-ouvertes.fr/hal-00878222
Solution of axisymmetric Maxwell equations, Mathematical Methods in the Applied Sciences, vol.334, issue.10, pp.861-896, 2003. ,
DOI : 10.1002/mma.400
URL : https://hal.archives-ouvertes.fr/hal-00989564
Characterization of the singular part of the solution of Maxwell's equations in a polyhedral domain, Mathematical Methods in the Applied Sciences, vol.2, issue.6, pp.485-499, 1999. ,
DOI : 10.1002/(SICI)1099-1476(199904)22:6<485::AID-MMA46>3.0.CO;2-E
Numerical Solution to the Time-Dependent Maxwell Equations in Two-Dimensional Singular Domains: The Singular Complement Method, Journal of Computational Physics, vol.161, issue.1, pp.218-249, 2000. ,
DOI : 10.1006/jcph.2000.6499
URL : https://hal.archives-ouvertes.fr/hal-01010725
Resolution of the Maxwell equations in a domain with reentrant corners RAIRO Mathematical Modelling and Numerical Analysis, pp.359-389, 1998. ,
Weighted Cl??ment operator and application to the finite element discretization of the axisymmetric Stokes problem, Numerische Mathematik, vol.4, issue.1 ,
DOI : 10.1007/s00211-006-0039-9
Spectral methods for axisymmetric domains, Series in Applied Mathematics, Gauthiers-Villars, 1999. ,
Une méthode d'´ eléments finis pour la résolution des pro-bì emes elliptiques dans des ouverts avec coins, C. R. Acad. Sci. Paris, Sér. I, vol.293, p.99101, 1981. ,
Finite-Elemente-Verfahren zur numerischen L??sung elliptischer Differentialgleichungen auf Gebieten mit Ecken, Computing, vol.34, issue.1, 1982. ,
DOI : 10.1007/BF02237995
Espaces de Sobolev avec poids pour l'??quation de Laplace dans le demi-espace, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.328, issue.3, pp.221-226, 1999. ,
DOI : 10.1016/S0764-4442(99)80125-6
Coefficients of the singularities for elliptic boundary value problems on domains with conical points. III. Fiinite element methods on polygonal domains, SIAM J. Numer. Anal, vol.29, p.1, 1992. ,
A singular field method for Maxwell's equations SIAM, J. Numer. Anal, vol.59, issue.6, pp.2028-2044, 1999. ,
Elliptic boundary value problems of second order in piecewise smooth domains, 2006. ,
Multigrid methods for the computation of edge tensor product singular functions ,
Algebraic convergence for anisotropic edge elements in polyhedral domains, Numerische Mathematik, vol.31, issue.1, pp.29-65, 2005. ,
DOI : 10.1007/s00211-005-0607-4
A Finite Element Method Using Singular Functions for the Poisson Equation: Corner Singularities, SIAM Journal on Numerical Analysis, vol.39, issue.1, pp.286-299, 2001. ,
DOI : 10.1137/S0036142999355945
Asymptotic expansion of the solution of an interface problem in a polygonal domain with thin layer Asymptotic Analysis, 2006. ,
Couplage de modèles et de méthodes numériques pour l'´ electromagnétisme en domaine temporel, Revue Européenne des Eléments Finis, vol.8, pp.5-6, 1999. ,
Div-rot tools for solving Maxwell equations ,
The Fourier Singular Complement Method for the Poisson problem. Part I : prismatic domains The Fourier Singular Complement Method for the Poisson problem, Numerische Mathematik, vol.101102, pp.423-450, 2005. ,
URL : https://hal.archives-ouvertes.fr/hal-00094316
The Singular Complement Method for 2d scalar problems, Comptes Rendus Mathematique, vol.336, issue.4, pp.353-358, 2003. ,
DOI : 10.1016/S1631-073X(03)00030-X
Justification de la loi de Peek enélectrostatiqueenélectrostatique, C. R. Acad. Sci., Serie I, vol.343, 2006. ,
Multi-scaled asymptotic expansions for the electric potential : surface charge densities at rounded corners, Math. Mod. Meth. Appl. Sci, vol.17, issue.6, 2007. ,
Basic error estimates for elliptic problems Handbook of numerical analysis, 1991. ,
Singularities of Electromagnetic Fields??in Polyhedral Domains, Archive for Rational Mechanics and Analysis, vol.151, issue.3, pp.221-276, 1151. ,
DOI : 10.1007/s002050050197
Singularly perturbed mixed boundary value problem, Comm. Partial. Diff. Equations, vol.21, pp.11-12, 1996. ,
Weighted regularization of Maxwell equations in polyhedral domains, Numerische Mathematik, vol.93, issue.2, pp.239-278, 2002. ,
DOI : 10.1007/s002110100388
Singularities of Maxwell interface problems, ESAIM: Mathematical Modelling and Numerical Analysis, vol.33, issue.3, 1998. ,
DOI : 10.1051/m2an:1999155
Elliptic boundary value problems on corner domains, Lecture notes in mathematics, vol.1341, 1988. ,
DOI : 10.1007/BFb0086682
Numerical approximation of elliptic interface and corner problems Habilitationsschrift, 1981. ,
Eléments finis : Théorie, applications, mise en oeuvre Springer, 2002. ,
An Analysis of the Finite Element Method Prentice-Hall, 1973. ,
Résolution deséquationsdeséquations de Maxwell instationnaires avec charges dans des domaines non-convexes, Thèse detroisì eme cycle, 2002. ,
Etude de quelquesprobì emes aux limites extérieurs et résolution paréquations paréquations intégrales, Thèse de Doctorat d'Etat, 1987. ,
Singular solutions of elliptic boundary value problems in polyhedra, Portugaliae Mathematica, vol.41, pp.1-4, 1982. ,
Elliptic problems in nonsmooth domains Monographs and studies in mathematics, 1985. ,
Edge Behavior of the Solution of an Elliptic Problem, Mathematische Nachrichten, vol.34, issue.1, pp.281-299, 1987. ,
DOI : 10.1002/mana.19871320119
Singularities in boundary value problems RMA 22, 1992. ,
Espaces de Sobolev avec poids Application auprobì eme de Dirichlet dans un demi espace, Rend. Sem. Univ. Padova, vol.46, pp.227-272, 1971. ,
Singularity functions at axisymmetric edges and their representation by Fourier series, Mathematical Methods in the Applied Sciences, vol.8, issue.12, pp.837-854, 1993. ,
DOI : 10.1002/mma.1670161202
The Fourier-Finite-Element Method for Poisson???s Equation in Axisymmetric Domains with Edges, SIAM Journal on Numerical Analysis, vol.33, issue.5, pp.1885-1911, 1996. ,
DOI : 10.1137/S0036142994266108
Résolution deséquationsdeséquations de Maxwell avec desélémentsdeséléments finis de Galerkin continus, Thèse detroisì eme cycle, Ecole Polytechnique, 2005. ,
Steidten Das Multigrid-Programmsystem FEMGP zur Lösung elliptischer und parabolischer Differentialgleichungen (Programmdokumentation), Technische Universität Chemnitz ,
Coins et arrondis enélémentsenéléments finis Une approche mathématique des coins et arrondis pour les solutions parélémentsparéléments finis de l'´ equation de Laplace, RIGE, vol.8, pp.35-45, 2005. ,
M??thode de calcul du coefficient de singularit?? pour la solution du probl??me de Laplace dans un domaine di??dral, ESAIM: Mathematical Modelling and Numerical Analysis, vol.27, issue.4, pp.395-420, 1993. ,
DOI : 10.1051/m2an/1993270403951
Equations intégrales etprobì emes de diffraction, 2004. ,
Résolution numérique duprobì eme du potentiel dans le plan, Thèse de l'université de Rennes, 1974. ,
Probì emes aux limites non homogènes et applications, 1968. ,
Méthode de fonctionssingulì eres pourprobì emes aux limites avec singularités d'arêtes, C. R. Acad. Sci. Paris Sér. I Math, vol.319, p.11091114, 1994. ,
Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Problems : Volume I Operator Theory, Advances and Applications, vol.111, 2000. ,
Plamenevskii Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Problems : Volume 2 Operator Theory, Advances and Applications, vol.111, 2000. ,
Résolution d'unprobì eme aux limites dans un ouvert axisymétrique parélémentsparéléments finis en r, z et séries de Fourier en ?. RAIRO Analyse Numérique, pp.405-461, 1982. ,
Sur quelqueséquationsquelqueséquations aux dérivées partielles et leur analyse numérique, Thèse de doctorat, 2004. ,
Sur l'approximation des solutions duprobì eme de Dirichlet dans un ouvert avec coin Singularities and constructive methods for their treatment, pp.199-206, 1121. ,
Elliptic Problems in Domains with Piecewise Smooth Boundaries, De Gruyter Expositions in Mathematics, vol.13, 1994. ,
DOI : 10.1515/9783110848915
Les méthodes directes en théorie deséquationsdeséquations elliptiques, 1967. ,
Variacionno-raznostnye metody re? senija ellipti? ceskich uravnenij, Izd. Akad. Nauk Armjanskoj SSR, 1979. ,
Asymptotics and special functions Academic Press ,
Singularities of the Laplacian at corners and edges of three-dimensional domains and their treatment with finite element methods, Mathematical Methods in the Applied Sciences, vol.20, issue.3, pp.339-350, 1988. ,
DOI : 10.1002/mma.1670100309
Analyse et analyse numérique des singularités enélectromagnétismeenélectromagnétisme, Thèse detroisì eme cycle, 2003. ,
Analyse multi-´ echelle et conditions aux limites approchées pour unprobì eme avec couche mince dans un domainè a coin Thèse de doctorat, 2003. ,
Efficiency of approximate boundary conditions for corner domains coated with thin layers, Comptes Rendus Mathematique, vol.340, issue.3, pp.215-220, 2005. ,
DOI : 10.1016/j.crma.2004.12.011
Die Fourier-Finite-Elemente-Methode für elliptische Interfaceprobleme in axialsymmetrischen Gebieten, 1994. ,